The time, t, required to empty a tank varies inversely as the rate, r, of pumping. if a pump can empty a tank in 2.5 hours at a rate of 400 gallons per minute, how long will it take to empty a tank at 500 gallons per minute?

Variation can be direct, inverse and joint.

It will take 2 hours to empty the tank at a rate of 500 gallons per minutes

Let time be represented with t, and r represent rate.

The inverse variation is represented as:

Represent as an equation

Make k the subject

When t = 2.5 and r = 400, we have:

When r = 500, we have:

Divide both sides by 500

Rewrite as:

Hence, it will take 2 hours to empty the tank at a rate of 500 gallons per minutes

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